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L H S
√(cosec theeta-1)/(cosec the eta+1)+
√(cosec the eta+1)/(cosec theeta-1)
={√(cosec theeta-1)^2+√(cosec the eta+1)^2}/
√(cosec the eta+1).(cosec theeta-1)
=(cosec theeta-1+cosec theeta+1)/√(cosec^2theeta-1)
=2cosec theeta/√cot^2theeta
=2cosec theeta/cot theeta
=2.1/sin theeta.sin theeta/cos theeta
=2/cos theeta
=2sec theeta
=RHS
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Hence Proved
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